Concepts of null correlation

Concepts of null correlation for r-compositions are discussed in this chapter, following the methodology developed by J. Aitchison for the statistical analysis of compositional data. This will be combined with G. Matheron’s theory of regionalized variables. These concepts are to be understood in the sense of absence de correlation différée (absence of deferred correlation), as defined by Matheron (1965). Concepts of null correlation are important not only for spatial-structure analysis of r-compositions, but also for simulation of phenomena that can be described by the use of r-compositions. The intrinsic analogue to the definitions of null correlation in the secondorder stationary case is carried out in parallel in this chapter because the relation between them is of special interest. All of the following concepts depend in general on the length of the vector h and also on its direction and sign, that is, they can be defined depending on the length, or set of lengths, and the direction, or set of directions, of h, or both. Therefore, as in Chapter 3, statements will be made for h Î H, where H stands for a set of vectors with specified range of directions and range of lengths. Here, for example, H may contain all possible directions and lengths for h, except h = 0; in this case, statements will be valid only in a spatial sense, but not in a standard nonspatial sense.